Logarithms involving decimals

Question

I am a student wondering how would I put this correctly into a calculator.

I have 1,05 and 1,216

1,05^n=1,216

How would I calculate n without just multiplying 1,05 against itself until I hit the desired result.I know that n=4 but how would I calculate this easier?

All tips and help is appreciated.

Thank you in advance!

Answer 1

$$n=\frac{\ln(1.216)}{\ln(1.05)}=\frac{\log(1.216)}{\log(1.05)}$$

Answer 2

$n$ is approximately $4$ not $n=4$. because $1.05^4=1.21550625 \neq 1.216$. Therefore you can not find n by multiplying $1.05$ by itself n times to get $1.216$. calculate n using the logarithm function of the calculator.